homoeomorphous Synonyms
No Synonyms and anytonyms found
homoeomorphous Meaning
Webster
homoeomorphous (a.)
Manifesting homoeomorphism.
homoeomorphous Sentence Examples
- The surface of a cylinder and a plane are homoeomorphous, meaning they can be smoothly deformed into each other without cutting or gluing.
- The unit square and the unit circle are homoeomorphous, demonstrating that two figures with very different shapes can still have the same topological properties.
- Homoeomorphous objects have the same number of holes, handles, and connected components.
- A sphere and a cube are not homoeomorphous because the sphere has no holes while the cube has six.
- Homoeomorphism is a fundamental concept in topology, allowing the classification of surfaces and higher-dimensional objects.
- The topology of a manifold is determined by its homoeomorphism class, which reflects its basic geometric properties.
- In algebraic topology, homoeomorphous objects have isomorphic homology and cohomology groups.
- The topological invariance of homoeomorphism means that it is unaffected by continuous deformations.
- Homoeomorphism is used in the study of knots and braids, where it provides insights into their topological complexity.
- Differential topology extends the concept of homoeomorphism to manifolds with smooth structures, offering powerful tools for analyzing the geometry of curved surfaces.
FAQs About the word homoeomorphous
Manifesting homoeomorphism.
No synonyms found.
No antonyms found.
The surface of a cylinder and a plane are homoeomorphous, meaning they can be smoothly deformed into each other without cutting or gluing.
The unit square and the unit circle are homoeomorphous, demonstrating that two figures with very different shapes can still have the same topological properties.
Homoeomorphous objects have the same number of holes, handles, and connected components.
A sphere and a cube are not homoeomorphous because the sphere has no holes while the cube has six.
